A multiple-input multiple-output (MIMO) communication system employs multiple (NT) transmit antennas and multiple (NR) receive antennas for data transmission. A MIMO channel formed by the NT transmit and NR receive antennas may be decomposed into NS independent channels, with NS≦min {NT, NR}. Each of the NS independent channels is also referred to as a spatial sub-channel of the MIMO channel and corresponds to a dimension. The MIMO system can provide improved performance (e.g., increased transmission capacity) over that of a single-input single-output (SISO) communication system if the additional dimensionalities created by the multiple transmit and receive antennas are utilized.
A wideband MIMO system typically experiences frequency selective fading, i.e. different amounts of attenuation across the system bandwidth. This frequency selective fading causes inter-symbol interference (ISI), which is a phenomenon whereby each symbol in a received signal acts as distortion to subsequent symbols in the received signal. This distortion degrades performance by impacting the ability to correctly detect the received symbols. As such, ISI is a non-negligible noise component that may have a large impact on the overall signal-to-noise-and-interference ratio (SNR) for systems designed to operate at high SNR levels, such as MIMO systems. In such systems, equalization may be used at the receivers to combat ISI. However, the computational complexity required to perform equalization is typically significant or prohibitive for most applications.
Orthogonal frequency division multiplexing (OFDM) may be used to combat ISI without the use of computationally intensive equalization. An OFDM system effectively partitions the system bandwidth into a number of (NF) frequency sub-channels, which may be referred to as sub-bands or frequency bins. Each frequency sub-channel is associated with a respective subcarrier frequency upon which data may be modulated. The frequency sub-channels of the OFDM system may experience frequency selective fading (i.e., different amounts of attenuation for different frequency sub-channels) depending on the characteristics (e.g., multipath profile) of the propagation path between transmit and receive antennas. With OFDM, the ISI due to the frequency selective fading may be combated by repeating a portion of each OFDM symbol (i.e., appending a cyclic prefix to each OFDM symbol), as is known in the art. A MIMO system may thus advantageously employ OFDM to combat ISI.
In order to increase the transmission data rate and spectral efficiency of the system, spatial multiplexing may be applied at the transmitter where different and independent data streams may be communicated over a plurality of spatial sub-channels. The detection accuracy of the receiver can be severely degraded due to a strong multiple access interference (interference of data streams transmitted from different antennas). Moreover, spatial and frequency sub-channels may experience different channel conditions (e.g., fading and multipath effects) and may achieve different SNRs. Also, channel conditions may vary over time.
Different techniques can be applied at the receiver to accurately detect information data transmitted from a plurality of antennas over spatial and frequency sub-channels. Suppression of the multiple access interference in MIMO-OFDM system can be achieved by applying maximum likelihood (ML) detection at the receiver.
The ML detection is optimal algorithm in terms of accuracy because likelihoods of all symbol vectors that can be possibly transmitted from a plurality of antennas may be evaluated. On the other side, computational complexity may be large especially in systems with high spectral efficiency that employ large number of transmit antennas and high-order modulation types.
The Log-MAP (maximum a posteriori) ML detection can be considered as an ideal maximum-likelihood algorithm in terms of error rate performance. It utilizes squared l2 norm as a metric for calculation of log-likelihood ratios (hereinafter abbreviated as LLRs) of coded transmission bits. Complexity of direct computation of squared l2 norms may be large, especially for high order modulation types and/or high dimensional Multiple-Input Multiple-Output (MIMO) wireless systems. Due to a high computational complexity of the Log-MAP ML algorithm, the Max-Log-MAP approach for ML detection may be preferred for actual hardware implementation where summation operations can be replaced with comparison operations. But, this approach also requires computation of squared l2 norms.
Therefore, there is a need in the art to reduce computational complexity of the Max-Log-MAP based ML detection in systems with high spectral efficiency.